This project focuses on the formulation, analysis, and interpretation of mathematical models which describe biological waves and oscillations. The main topics of interest are: (i) neuronal networks and their application to the understanding of various nonlinear neuronal phenomena such as phosphenes, hallucinations, and epilepsy; (ii) excitable and oscillatory systems and their behavior under periodic forcing; (iii) general theories of stationary, homogeneous media; (iv) chains of oscillators useful in modeling intestinal and gastric waves. Our prime objective is to expose the qualitative behavior of the models as an explanation for observed biological patterns.